Why do Firefox, Preferred Applications and x-www-browser disagree on default browser?

Honestly, I don't know where the Firefox / Preferred Application setting lives. However, x-www-browser is managed by the "alternatives" system in dpkg. You can interactively change it by typing this at a command prompt:

sudo update-alternatives --config x-www-browser

So, not a complete answer but might let you straighten things out and move on :)

Update This page describes where Gnome keeps its preferred applications settings. The page refers to Linux Mint, but the same principles should apply: http://www.libre-software.net/change-the-default-application-linux-mint-ubuntu

So yes, they're different.